Let me preface this by saying that I do not like the term "purely positive", and I generally avoid any use of it. In fact, I find it to be moderately aversive, in spite of the fact that my own training approach could technically be termed as such. However, because it is a term that is used commonly, both by those who choose to incorporate correction into their training, and by the general pet public, I believe that consideration of the term is in order.
In behavior theory speak, the term "purely positive" is used to designate dog trainers who train, almost exclusively, using positive reinforcers (incorporating limited use of negative punishment where needed), and who deliberately avoid all use of positive punishment and negative reinforcement. In common speak, "purely positive" means that the trainer uses things that the dog likes as rewards to help the dog learn, and avoids things that the dog finds unpleasant, aversive, or painful.
But in actual practice, I find that "purely positive" tends to be used much more as a statement of what the trainer is not doing - correcting the dog - than a clear description of what the trainer actually is doing, which can be quite systematic and effective. This tends to give the incorrect impression that the "purely positive" trainer is actually not doing much of anything!
One of the main reasons why I find the term aversive is because I have heard it thrown in the face of primarily positive reinforcement based trainers (hereafter designated as PR+) as an attempt to discredit their training methods, based not on actual results that the trainer may or may not have achieved using PR+ methods, but on the often repeated mantra: no training can be purely positive all the time.
Technically, that is true. No training can be "purely positive" all the time. Sometimes an approach that the trainer intends to be reinforcing to the dog turns out to be aversive to a particular dog. And there are times when an individual trainer may not pick up on that. Accidents that are aversive to the dog happen - things fall over, paws get stepped on, trainer timing is sometimes off and feedback to the dog can be unclear, etc. And, there are times when restricting the dog's access to something that he or she might want is necessary. In other words, even when the trainer is committed to a PR+ approach, everything is not pleasant for the dog at all times.
PR+ trainers are well aware of all of this. The aim of PR+ training is not to make everything pleasant for the dog at all times, but to facilitate canine learning, primarily, though methods that employ the use of positive reinforcement. This is an important distinction. I would say that the vast majority of trainers, regardless of training method chosen, ultimately want to make life as pleasant as possible for their dogs. And it is a fact that there are times in the learning process, and in life itself, when the dog will experience times of difficulty and frustration, and when he will not always have what he wants. And while PR+ trainers do make a deliberate choice to avoid use of training techniques that use aversion to teach concepts and behavior, they also know that training is a discipline that often presents challenges to the dog along the way. In other words, of course, no training is "purely positive" all the time, in the sense that no training is 100% pleasant to the dog at all times.
This, however, does not change the fact that there are many, many good PR+ trainers out there who get excellent results. I propose that the effectiveness of PR+ training methods should be judged on the basis of the actual results that competent PR+ trainers produce, and not on implications associated with a term that does not precisely describe this type of training to begin with.
Another reason why I avoid the use of the term "purely positive" is that the term is used to mischaracterize PR+ trainers as "cookie pushers" who lack any clear purpose, structure, or use of intellect in their training. I often hear things like, "a dog won't stop for a cookie when he is busy chasing a squirrel". As if PR+ trainers are outside, pointlessly calling "cookie, cookie, cookie" while waving a hot dog in the air, as the dog is tearing away full speed and then call that a training method! There are certainly those who have that impression when they hear the term "purely positive"!
PR+ training is highly structured, the methods that fall under the umbrella of PR+ have clear purpose, and PR+ trainers know how to develop training plans that take the individual needs of the dog into account. A good PR+ trainer would no more recommend the above approach than he or she would recommend that a skydiving instructor should wait until the skydiving student is falling from the plane before explaining how the parachute works!
Finally, "purely positive" is often understood to mean, simply, "never say no". For many the term is synonymous with "let the dog do whatever he wants and when you like something he does, give him a cookie, and ignore absolutely everything else". So, if the dog is running toward a busy street, ignore it; if the dog is about to eat a fully cooked chicken that is sitting on the counter, ignore it; if the dog poops all over the house, ignore it; if the dog is bullying other dogs in the house, ignore it. This is absolutely not what happens when one trains using PR+!
In reality, the PR+ trainer would view these scenarios more like this: if the dog is running toward a busy street, use a well trained recall to call the dog back; if the dog is about to eat a fully cooked chicken that is sitting on the counter, use a well trained leave it cue to indicate that it should be left alone; if the dog poops all over the house, go back to training 101 and teach the dog to go to the bathroom outdoors (unless it's a medical issue, of course, in which case, consult a vet); if the dog is bullying other dogs in the house, assess and address the situation to ensure the well being of all of the dogs. And while the PR+ trainer will choose to use positive reinforcers to teach the excellent recall, the well-understood "leave it", and a combination of positive reinforcement/negative punishment to teach the dog where to defectate and how to behave appropriately around the other dogs, the idea of that the "purely positive" trainer is sitting around letting it all happen is simply false.
I believe that this misconception has developed from an incorrect understanding of the free shaping training technique. Yes, when one is free shaping, the trainer allows the dog to do anything he or she chooses and then clicks and gives a treat when the dog does something that the trainer wants. Through this process, the dog learns what is being clicked frequently and begins to offer that behavior, and then that offering is "shaped" into a concrete behavior that is put on a cue. This can be done to teach basic behaviors, tricks, and sport skills.
It is important to note that free shaping is done within the context of training sessions, not throughout life in general. Free shaping should be done in situations where the dog is going to be safe no matter what he or she should choose to do, like a living room or other training space. Free shaping is not done with the untrained dog off leash next to a busy street. And, of course, if the dog is going to do something that is unsafe during a free shaping session, the dog is not left to do that unsafe thing in the name of shaping!
In reality, dogs who are trained through PR+ methods learn to ignore cars that they would have formerly chased, they learn to recall off of squirrels and other exciting things, they learn to greet people and other dogs politely, they are housetrained, they learn what is theirs to chew and what is not a chew toy, they learn to walk politely on loose leashes, etc. etc. etc.
PR+ training is all about the dog learning how to be a good citizen in the human world, how to be a polite member of a human household, how to carry out a set of tasks to assist us with our work, or, sometimes, how to be a skilled and competent participant in a human-made dog sport.
"Purely positive" expresses none of this, and implies a good deal that is actually not true.
I am all for abandoning the term entirely in favor of finding more precise ways of describing what PR+ training is really about! I like "Primarily Positive Reinforcement Based Training" (PR+) myself. That expresses the strong emphasis on positive reinforcement, but leaves the door open for a discussion of what "primarily" means exactly to an individual trainer, as well as what else one might incorporate (such as negative reinforcement) and when and why.